Mine are not joysticks but gamepads
So I got a few Arduinos / teensy boards in to experiment, on the back of work from others I've got my sidewinder GamePad working via USB through a Sparkfun Pro Micro(arduino leonardo compatible), little bit of code that uses serial input from the Sidewinder and coverts it into keyboard inputs to the computer via USB, Played some Streets of Rage 4 with it, just need to get the timing right n tweak the code, (most of the code is not mine and the code that is mine is probably super inefficient).
there's projects ready for the sticks, but none included the gamepad for some reason.
Next step is getting it working as an actual joystick/gamepad rather than just keyboard input, but need more research on that and the Teensy board should be a better fit for that than the Pro Micro.
Still proof of concept is there and it works as keyboard input.
(Keys bound: ESC(Start) W A S D(DPAD) Q(Left Trigger) E(Right Trigger) U(X button) I(Y button) O(Z button) J(A button) K(B button) L(C Button) SPACE( M Button))
Code isn't ready yet as the timing needs sorted(too fast without delays causes input issues).
Also no implementation of the controller pass-through port, would need to probe around to see how the second / third / fourth chained controllers communicate through the first controller.